Wait, you have proof that you sent them - in your sent box, but you no longer have copies of the papers? Why not just print them out again & show her that you sent them on whatever date it was? That you slipped a copy under the door is based only on your word, unless you received some confirmation from her that she received them. Again, you should have a copy of that confirmation.
No offense meant, I'm sure you wouldn't be lying to us to get our sympathy, but in my experience as a teacher, I've had quite a few cases of "I put it on your desk when you weren't in the room." As unorganized as my desk may look, I don't lose things. Misplaced momentarily, but lost? Never. I don't even throw out scrap paper until after each quarter - so that I'm never in a situation wondering "well, maybe I accidentally put it in the recycle bin?" And, almost without exception, the students claiming they left (whatever it is) for me are students who have missed other assignments. In the case of major assignments like a paper, after I apologize for possibly losing it and "tell you what, go print off another copy & I'll be happy to grade it right now without any penalty for being late" - invariably, their hard drive was reformatted, or their dog chewed up the hard drive, or...
Thus, while you may be telling the truth, there are so many students who tell the same story as a lie, it's going to be hard to get your story to be believed.